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Eugenio Onate - One of the best experts on this subject based on the ideXlab platform.
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improvements in the membrane behaviour of the three node rotation free bst shell triangle using an assumed strain approach
Computer Methods in Applied Mechanics and Engineering, 2005Co-Authors: Fernando G Flores, Eugenio OnateAbstract:In this paper an assumed strain approach is presented in order to improve the membrane behaviour of a thin shell triangular element. The so called Basic Shell Triangle (BST) has three nodes with only translational degrees of freedom and is based on a Total Lagrangian Formulation. As in the original BST element the curvatures are computed resorting to the surrounding elements (patch of four elements). Membrane strains are now also computed from the same patch of elements which leads to a non-conforming membrane behaviour. Despite this non-conformity the element passes the patch test. Large strain plasticity is considered using a logarithmic strain–stress pair. A plane stress behaviour with an Additive Decomposition of elastic and plastic strains is assumed. A hyperplastic law is considered for the elastic part while for the plastic part an anisotropic quadratic (Hill) yield function with non-linear isotropic hardening is adopted. The element, termed EBST, has been implemented in an explicit (hydro-)code adequate to simulate sheet-stamping processes and in an implicit static/dynamic code. Several examples are given showing the good performance of the enhanced rotation-free shell triangle. � 2004 Elsevier B.V. All rights reserved.
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improvements in the membrane behaviour of the three node rotation free bst shell triangle using an assumed strain approach
Computer Methods in Applied Mechanics and Engineering, 2005Co-Authors: Fernando G Flores, Eugenio OnateAbstract:Abstract In this paper an assumed strain approach is presented in order to improve the membrane behaviour of a thin shell triangular element. The so called Basic Shell Triangle (BST) has three nodes with only translational degrees of freedom and is based on a Total Lagrangian Formulation. As in the original BST element the curvatures are computed resorting to the surrounding elements (patch of four elements). Membrane strains are now also computed from the same patch of elements which leads to a non-conforming membrane behaviour. Despite this non-conformity the element passes the patch test. Large strain plasticity is considered using a logarithmic strain–stress pair. A plane stress behaviour with an Additive Decomposition of elastic and plastic strains is assumed. A hyperplastic law is considered for the elastic part while for the plastic part an anisotropic quadratic (Hill) yield function with non-linear isotropic hardening is adopted. The element, termed EBST, has been implemented in an explicit (hydro-)code adequate to simulate sheet-stamping processes and in an implicit static/dynamic code. Several examples are given showing the good performance of the enhanced rotation-free shell triangle.
Patrizio Neff - One of the best experts on this subject based on the ideXlab platform.
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A canonical rate-independent model of geometrically linear isotropic gradient plasticity with isotropic hardening and plastic spin accounting for the Burgers vector
Continuum Mechanics and Thermodynamics, 2019Co-Authors: Francois Ebobisse, Klaus Hackl, Patrizio NeffAbstract:In this paper, we propose a canonical variational framework for rate-independent phenomenological geometrically linear gradient plasticity with plastic spin. The model combines the Additive Decomposition of the total distortion into non-symmetric elastic and plastic distortions, with a defect energy contribution taking account of the Burgers vector through a dependence only on the dislocation density tensor $${{\,\mathrm{Curl}\,}}p$$ Curl p giving rise to a non-symmetric nonlocal backstress, and isotropic hardening response only depending on the accumulated equivalent plastic strain. The model is fully isotropic and satisfies linearized gauge invariance conditions, i.e., only true state variables appear. The model satisfies also the principle of maximum dissipation which allows to show existence for the weak formulation. For this result, a recently introduced Korn’s inequality for incompatible tensor fields is necessary. Uniqueness is shown in the class of strong solutions. For vanishing energetic length scale, the model reduces to classical elasto-plasticity with symmetric plastic strain $$\mathbf \varepsilon _p$$ ε p and standard isotropic hardening.
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a canonical rate independent model of geometrically linear isotropic gradient plasticity with isotropic hardening and plastic spin accounting for the burgers vector
arXiv: Analysis of PDEs, 2016Co-Authors: Francois Ebobisse, Klaus Hackl, Patrizio NeffAbstract:In this paper we propose a canonical variational framework for rate-independent phenomenological geometrically linear gradient plasticity with plastic spin. The model combines the Additive Decomposition of the total distortion into non-symmetric elastic and plastic distortions, with a defect energy contribution taking account of the Burgers vector through a dependence only on the dislocation density tensor Curl(p) giving rise to a non-symmetric nonlocal backstress, and isotropic hardening response only depending on the accumulated equivalent plastic strain. The model is fully isotropic and satisfies linearized gauge-invariance conditions, i.e., only true state-variables appear. The model satisfies also the principle of maximum dissipation which allows to show existence for the weak formulation. For this result, a recently introduced Korn's inequality for incompatible tensor fields is necessary. Uniqueness is shown in the class of strong solutions. For vanishing energetic length scale, the model reduces to classical elasto-plasticity with symmetric plastic strain sym(p) and standard isotropic hardening.
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numerical approximation of incremental infinitesimal gradient plasticity
International Journal for Numerical Methods in Engineering, 2009Co-Authors: Patrizio Neff, Antje Sydow, Christian WienersAbstract:We investigate a representative model of continuum infinitesimal gradient plasticity. The formulation is an extension of classical rate-independent infinitesimal plasticity based on the Additive Decomposition of the symmetric strain tensor into elastic and plastic parts. It is assumed that dislocation processes contribute to the storage of energy in the material whereby the curl of the plastic distortion appears in the thermodynamic potential and leads to an additional nonlocal backstress tensor. The formulation is cast into a numerical framework by a saddle point approximation of the corresponding minimization problem in each incremental loading step. This allows one to reformulate the (nonlocal) dissipation inequality to a point-wise flow rule and yields a solution scheme, which is a direct extension of the standard approach in classical plasticity. Our numerical results show the regularizing effects of the additional physically motivated terms. Copyright © 2008 John Wiley & Sons, Ltd.
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Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility
International Journal of Solids and Structures, 2003Co-Authors: Stefan Hartmann, Patrizio NeffAbstract:Abstract In this article we investigate several models contained in the literature in the case of near-incompressibility based on invariants in terms of polyconvexity and coerciveness inequality, which are sufficient to guarantee the existence of a solution. These models are due to Rivlin and Saunders, namely the generalized polynomial-type elasticity, and Arruda and Boyce. The extension to near-incompressibility is usually carried out by an Additive Decomposition of the strain energy into a volume-changing and a volume-preserving part, where the volume-changing part depends on the determinant of the deformation gradient and the volume-preserving part on the invariants of the unimodular right Cauchy–Green tensor. It will be shown that the Arruda–Boyce model satisfies the polyconvexity condition, whereas the polynomial-type elasticity does not. Therefore, we propose a new class of strain-energy functions depending on invariants. Moreover, we focus our attention on the structure of further isotropic strain-energy functions.
Fernando G Flores - One of the best experts on this subject based on the ideXlab platform.
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improvements in the membrane behaviour of the three node rotation free bst shell triangle using an assumed strain approach
Computer Methods in Applied Mechanics and Engineering, 2005Co-Authors: Fernando G Flores, Eugenio OnateAbstract:In this paper an assumed strain approach is presented in order to improve the membrane behaviour of a thin shell triangular element. The so called Basic Shell Triangle (BST) has three nodes with only translational degrees of freedom and is based on a Total Lagrangian Formulation. As in the original BST element the curvatures are computed resorting to the surrounding elements (patch of four elements). Membrane strains are now also computed from the same patch of elements which leads to a non-conforming membrane behaviour. Despite this non-conformity the element passes the patch test. Large strain plasticity is considered using a logarithmic strain–stress pair. A plane stress behaviour with an Additive Decomposition of elastic and plastic strains is assumed. A hyperplastic law is considered for the elastic part while for the plastic part an anisotropic quadratic (Hill) yield function with non-linear isotropic hardening is adopted. The element, termed EBST, has been implemented in an explicit (hydro-)code adequate to simulate sheet-stamping processes and in an implicit static/dynamic code. Several examples are given showing the good performance of the enhanced rotation-free shell triangle. � 2004 Elsevier B.V. All rights reserved.
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improvements in the membrane behaviour of the three node rotation free bst shell triangle using an assumed strain approach
Computer Methods in Applied Mechanics and Engineering, 2005Co-Authors: Fernando G Flores, Eugenio OnateAbstract:Abstract In this paper an assumed strain approach is presented in order to improve the membrane behaviour of a thin shell triangular element. The so called Basic Shell Triangle (BST) has three nodes with only translational degrees of freedom and is based on a Total Lagrangian Formulation. As in the original BST element the curvatures are computed resorting to the surrounding elements (patch of four elements). Membrane strains are now also computed from the same patch of elements which leads to a non-conforming membrane behaviour. Despite this non-conformity the element passes the patch test. Large strain plasticity is considered using a logarithmic strain–stress pair. A plane stress behaviour with an Additive Decomposition of elastic and plastic strains is assumed. A hyperplastic law is considered for the elastic part while for the plastic part an anisotropic quadratic (Hill) yield function with non-linear isotropic hardening is adopted. The element, termed EBST, has been implemented in an explicit (hydro-)code adequate to simulate sheet-stamping processes and in an implicit static/dynamic code. Several examples are given showing the good performance of the enhanced rotation-free shell triangle.
Augusto Ferrante - One of the best experts on this subject based on the ideXlab platform.
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the discrete time generalized algebraic riccati equation order reduction and solutions structure
Systems & Control Letters, 2015Co-Authors: Lorenzo Ntogramatzidis, Augusto FerranteAbstract:Abstract In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati equation arising in optimal control and optimal filtering problems into two parts corresponding to an Additive Decomposition X = X 0 + Δ of each solution X : The first part is trivial, in the sense that it is an explicit expression of the addend X 0 which is common to all solutions, so that it does not depend on the particular X . The second part can be–depending on the structure of the considered generalized Riccati equation–either a reduced-order discrete-time regular algebraic Riccati equation whose associated closed-loop matrix is non-singular, or a symmetric Stein equation. The proposed reduction is explicit, so that it can be easily implemented in a software package that uses only standard linear algebra procedures.
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the discrete time generalized algebraic riccati equation order reduction and solutions structure
arXiv: Optimization and Control, 2014Co-Authors: Lorenzo Ntogramatzidis, Augusto FerranteAbstract:In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati equation arising in optimal control and optimal filtering problems into two parts corresponding to an Additive Decomposition X=X0+D of each solution X: The first part is an explicit expression of the addend X0 which is common to all solutions, and does not depend on the particular X. The second part can be either a reduced-order discrete-time regular algebraic Riccati equation whose associated closed-loop matrix is non-singular, or a symmetric Stein equation.
Jacob Fish - One of the best experts on this subject based on the ideXlab platform.
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On the equivalence between the multiplicative hyper-elasto-plasticity and the Additive hypo-elasto-plasticity based on the modified kinetic logarithmic stress rate
Computer Methods in Applied Mechanics and Engineering, 2018Co-Authors: Yang Jiao, Jacob FishAbstract:Abstract In two theorems presented herein, we prove and subsequently demonstrate in several numerical examples involving homogeneous deformation that for isotropic materials, hyper-elasto-plasticity models based on the multiplicative Decomposition of the deformation gradient coincide with an Additive hypo-elasto-plasticity model (see Section 3.2) that employs the spin tensor based on the modified kinetic logarithmic rate. In the absence of strain-induced anisotropy (characterized by kinematic hardening herein), this objective stress rate coincides with the kinetic logarithmic rate recently developed by Jiao and Fish, 2017. We also show that other well-known Additive Decomposition models, such as those based on the Jaumann and logarithmic rates, may considerably deviate from the multiplicative model.
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Is an Additive Decomposition of a rate of deformation and objective stress rates passé
Computer Methods in Applied Mechanics and Engineering, 2017Co-Authors: Yang Jiao, Jacob FishAbstract:Abstract The manuscript critically examines a half a century old idea of decomposing the rate of deformation into elastic and plastic parts. We show that even the most recent Additive variant based on the logarithmic rate is inconsistent with the notion of elasticity in so-called unloading stress ratchetting obstacle test while the earlier corotational variants based on the Jaumann and Green–Naghdi rates are well known not to be integrable. We then propose a stress-dependent so-called kinetic logarithmic stress rate that is both integrable and passes the unloading stress ratchetting obstacle test. We also demonstrate that the Additive hypo-elasto-plasticity model based on the proposed kinetic logarithmic rate is weakly invariant under isochoric reference change for simple materials in the sense of Noll.